Download MAT-642

MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
SYLLABUS
MAT-642
(3L+1T+0P)
Integral Equations
4 Credits
Definition and classification, conversion of initial and boundary value problems to an integral
equation, Eigen-Values and Eigen functions. Solutions of homogeneous and general
Fredholm integral equations of second kind with separable kernels.
Solution of Fredholm and Volterra integral equations of second kind by methods of
successive substitutions and successive approximations, Resolvent kernel and its results.
Integral equations with symmetric kernels: Complex Hilbert space, Orthogonal system of
functions, fundamental properties of eigen values and eigen functions for symmetric kernels,
expansion in eigen-functions and bilinear forms, Hilbert-Schmidt theorem. Solution of
Fredholm integral equations of second kind by using Hilbert-Schmidt theorem. Fredholm
theorems. Solution of Volterra integral equations with convolution type kernels by Laplace
transform.
Books recommended:
1. W. V. Lovitte ,Linear Integral Equations, over Publications; Reissue edition , (2005).
2. R. P. Kanwal ,Linear Integral Equations, Birkhäuser; 2nd edition , (1996).
3 S.G. Mikhlin, Linear Integral Equations , Routledge, (1961).